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Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize…
Adiabatic quantum computers are a promising platform for approximately solving challenging optimization problems. We present a quantum approach to solving the balanced $k$-means clustering training problem on the D-Wave 2000Q adiabatic…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
Quantum computing leverages the unique properties of qubits and quantum parallelism to solve problems intractable for classical systems, offering unparalleled computational potential. However, the optimization of quantum circuits remains…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…
We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
For many practical applications of quantum computing, the most costly steps involve coherently accessing classical data. We help address this challenge by applying mass production techniques, which can reduce the cost of applying an…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
Computations show that the logic about a quantum factoring algorithm does not hold in reality on a D-Wave quantum computer. We demonstrate this for the integers 15 = 3 x 5, 91 = 7 x 13 and 899 = 29 x 31. The likely cause is the D-Wave…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of…
Quantum Computers, one fully realized, can represent an exponential boost in computing power. However, the computational power of the current quantum computers, referred to as Noisy Internediate Scale Quantum, or NISQ, is severely limited…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…